Explanation:
Sort the data in ascending order (essential for any quantile calculation):
2,600; 2,700; 2,800; 3,800; 4,300; 9,900
(n = 6 observations)
General position formula for the p-th quantile (common in FRM/GARP materials):
Position = (n + 1) × p
For 75% quantile → p = 0.75
Position = 7 × 0.75 = 5.25
Interpolate between the 5th and 6th observations:
5th value = 4,300
6th value = 9,900
75% quantile = 4,300 + 0.25 × (9,900 − 4,300) = 4,300 + 0.25 × 5,600 = 4,300 + 1,400 = 5,700
Ultimate access to all questions.
The following data represents a sample of daily profit of a sales company for six weeks in a particular year.
| Week | Amount of the Profit($) |
|---|---|
| 1 | 3,800 |
| 2 | 2,800 |
| 3 | 2,700 |
| 4 | 9,900 |
| 5 | 2,600 |
| 6 | 4,300 |
What is the 75% quantile profit?
A
3,000
B
5,700
C
3,300
D
3,700
